Final answer:
The temperature required for the gas to fill the balloon is approximately 89.9 Kelvin.
Step-by-step explanation:
To determine the temperature required for the gas to fill the balloon, we can use the ideal gas law equation:
PV = nRT
Where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.
Given that there are 0.0153 mol of gas, a volume of 1.37 L, and a pressure of 0.992 atm, we can rearrange the equation to solve for T:
T = PV / (nR)
Substituting in the values given:
T = (0.992 atm)(1.37 L) / (0.0153 mol)(0.0821 L atm/mol K)
T = 89.9 K
Therefore, the temperature required for the gas to fill the balloon is approximately 89.9 Kelvin.